It's hard to tell if you are kidding us. But it isn't April 1st so here goes:
Not all boats have shore power and an older C&C might not. But if your boat is so equipped, somewhere - usually near the transom- there is a plug in for 110 shore power. It will receive a three prong plug and mates with a 30 amp shore power chord. The other end of the chord plugs into the shore power source on the dock - another locking 3 prong plug. Depending on the quality of the installation and subsequent maintenance over the last forty years it may or may not be safe to turn it on. You should have the wiring checked by a qualified marine electrician.
I'll defer the solar question since I don't have such a system.
Instruments: Please forward specifics. Manufacturer, model, what the malfunction is. As a methodology I would first see if the units have power. If not I would test them with a portable power source before rewiring to see if they even power up. If they have power I would turn the attention to the sender's and their wiring and connections which are dubious in almost any installation. The the anemometer at the top of the mast - right? How do the wires go through the deck? It's likely they are in the mast and exit somewhere below the deck and attach to a terminal block. You can test the circuits there. If all else is good the anemometer can be replaced but it is pricey. At that point you have to consider new all around. Of course if the mast is down it's a lot easier.
Shore plumbing: I hate to disappoint you and I hope I've misunderstood you. I've never heard of this. If you have a holding tank, which isn't a certainty on this boat, there is a pump out deck fitting - marked "Waste" You probably have below waterline discharge even if you do have a holding tank. It is illegal to use almost anywhere.
I hope this is helpful. Others on this forum can give better information.